Calculate hydraulic gradient i = Δh/L from head drop and flow path length. Supports elevation + pressure mode, slope-angle conversion, and scenario presets.
The hydraulic gradient i = Δh / L is the rate at which total hydraulic head decreases along a flow path. It is the link between Darcy's law and real-world groundwater seepage, pipe friction losses, and open-channel slopes.
In groundwater engineering, the hydraulic gradient drives seepage velocity: the steeper the gradient, the faster water moves through soil. In pipe systems, i acts as the friction slope, and in uniform open-channel flow it aligns with the bed slope.
This calculator offers two modes. The simple mode uses head loss and path length directly. The detailed mode computes total head from upstream and downstream elevations and pressures, then derives the gradient. Results are shown as a dimensionless ratio, percent, permille, angle, and "1 in N" slope so the same answer can be read in whichever convention the project uses. That makes it easier to move between groundwater, pipe, and civil-design documents without reformatting the same slope by hand.
Use this calculator when you need to convert head loss into a gradient quickly and read the result in the notation used by different engineering disciplines.
It is useful for groundwater cross-sections, dam and levee checks, pipe-loss summaries, and any workflow where elevation and pressure data need to collapse into a single driving slope.
Hydraulic gradient: i = Δh / L Total head: h = z + p/(ρg) Where: • Δh = head difference between two points (m) • L = flow path length (m) • z = elevation (m) • p = gauge pressure (Pa) • ρ = fluid density (kg/m³) • g = gravitational acceleration (m/s²)
Result: i = 0.02 (2%)
i = 10/500 = 0.02. This means a 2% gradient — the head drops 2 meters for every 100 meters of flow path.
Hydraulic gradient is a small ratio, but it drives the whole problem. A modest change in head drop or flow length can materially change Darcy velocity, seepage risk, and friction-loss interpretation, so it helps to keep the geometry of the flow path explicit instead of treating the gradient as an abstract percentage.
The most common mistake is using straight-line distance when the true flow path is longer. Another is mixing pressure head and elevation head inconsistently when deriving total head from field measurements. For very small gradients, even a small surveying or piezometer error can move the result a lot in relative terms.
Natural groundwater gradients are usually very gentle: 0.001 to 0.01 (0.1–1%). Near pumping wells, gradients can be much steeper — 0.05 or more.
Darcy's law states q = K × i, where q is the specific discharge (m/s) and K is the hydraulic conductivity. The gradient i is the driving force for groundwater flow.
Essentially yes. In pipeline hydraulics, the friction slope Sf = hf / L, which is the hydraulic gradient due to friction losses. Under steady uniform flow in pipes, this equals the energy grade line slope.
The critical hydraulic gradient for piping (internal erosion) in sand is approximately i_cr = (γ_s - γ_w) / γ_w ≈ 1.0 for typical sands. Upward seepage at this gradient causes quicksand (boiling).
Civil engineers commonly express slopes as "1 in N" — one unit of vertical drop per N units of horizontal distance. A 1% slope is 1 in 100. Sewer grades are often specified this way.
L is the flow path length, not the straight-line distance. In tortuous aquifer paths, L may be longer than the map distance. In pipes, L is the actual pipe length including bends.